The second case. However I am hesitating to ask to look at the code of my supervisor. How would I explain why I need it (if it's not needed for my research)? It's also unlikely user-friendly, so it would take a lot of time to understand anything.

I think you touched on something important. Researchers are most concerned with “getting things working”.

One of my favorite points from the book Clean Code was that professional developers aren’t satisfied with “working code”, they aim to make it maintainable. Which may mean writing it in a way that is more clear and concise than we are used to